Adiabatic-following solutions for multisubband quantum wells excited by an ultrafast optical pump field

The two-band effective semiconductor optical Bloch equations for a quantum well have been generalized to include multisubband effects. The ultrafast transient adiabatic-following solutions are obtained from the equations for interband polarizations, intersubband polarizations, and subband-carrier distribution functions of a ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As/GaAs quantum well, excited by an ultrafast optical pump field. Two conservation laws for the multisubband case are derived. The steady-state response and the π-pulse response are studied. It is found that these multisubband equations lead to quantitatively different results from the conventional two-band approximation, particularly for wide quantum wells and asymmetric quantum wells.